Question: Riya is applying mulch to her garden. She applies it at a rate of $250{,}000\text{ cm}^3$ of mulch for every $\text{ m}^2$ of garden space. At what rate is Riya applying mulch in $\dfrac{\text{m}^3}{\text{m}^2}$ ?
Answer: We will convert $250{,}000\,\dfrac{\text{cm}^3}{\text{m}^2}$ to a rate in $\dfrac{\text{m}^3}{\text{m}^2}$ using the following conversion rates: There are $100\text{ cm}$ per $1\text{ m}$. Therefore, there are $(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3$ per $1\text{ m}^3$. $\begin{aligned} &\phantom{=}\dfrac{250{,}000\text{ cm}^3}{1\text{ m}^2} \cdot \dfrac{1\text{ m}^3}{1{,}000{,}000\text{ cm}^3} \\\\ &=\dfrac{250{,}000\cdot 1\cdot \cancel{\text{cm}^3} \cdot \text{m}^3}{1 \cdot 1{,}000{,}000 \cdot\text{m}^2\cancel{\text{cm}^3}} \\\\ &=\dfrac{250{,}000}{1{,}000{,}000}\,\dfrac{\text{m}^3}{\text{m}^2} \\\\ &=0.25\,\dfrac{\text{m}^3}{\text{m}^2} \end{aligned}$ In conclusion, the rate in $\dfrac{\text{m}^3}{\text{m}^2}$ at which Riya is applying mulch is: $0.25\,\dfrac{\text{m}^3}{\text{m}^2}$ [Why didn't we cancel the meters units?]